The announcement that the remaining 27 EU leaders had backed the plan came in a tweet from European Council president Donald Tusk barely 40 minutes after the meeting started.

And shortly afterwards Mrs May arrived at the council building in the Belgian capital to join the other leaders.

And now European Commission president Jean-Claude Juncker has warned Britain cannot expect to get a better Brexit deal if Parliament rejects the agreement hammered out by the Prime Minister.

Prime Minister Theresa May greets European Commission President Jean-Claude Juncker ahead of a working dinner at 10 Downing Street, London (Image: John Stillwell/PA Wire)

He said: "This is the deal. It's the best deal possible and the EU will not change its fundamental position when it comes to these issues.

Mr Juncker's comments were echoed Dutch prime minister Mark Rutte who urged MPs to give their approval in a vote expected to take place in the House of Commons, next month.

He said: "This is the deal on the table. I don't think there is anything more now. I don't want to contemplate a no vote. I think there will be a yes vote.

"I think this is the best we can all do - both Theresa May and her Government as well as the European Union.

"I do think she has everything now to argue for a yes vote in the British Parliament."

The EU's chief negotiator Michel Barnier said the deal was a "necessary step" to prepare for the next phase of negotiations which the Government hopes will result in a wide-ranging free trade agreement.

European Union chief Brexit negotiator Michel Barnier (Image: AP)

"Now it is time for everybody to take their responsibility. This deal is a necessary step to build the trust between the UK and the EU we need to build," Mr Barnier said.

"The next phase is an unprecedented and ambitious partnership. We will remain allies, partners and friends."

Ahead of the meeting Mrs May issued a direct plea to the public to support plan.

In a "letter to the nation", she said leaving the EU on March 29 2019 would mark "a new chapter in our national life" and there would be a moment of "renewal and reconciliation" after the bitter battles over Europe.

The almost 800-word message is an attempt to speak directly to the public to build support for her deal, which faces widespread opposition at Westminster including from both wings of her Conservative Party and the Democratic Unionist Party which props up her administration.

She said the deal "will honour the result of the referendum" by allowing the UK to "take back control" of its money, laws and borders.

"It is a deal for a brighter future, which enables us to seize the opportunities that lie ahead," she said.

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She promised she would be "campaigning with my heart and soul" to win the vote in the Commons.

And "with Brexit settled" the UK will be able to focus on the economy, NHS, building homes and tackling the "burning injustices" in society, the Prime Minister added.

The summit in Brussels is only taking place after Spain claimed the UK and EU had given into its demands for concessions over the future of Gibraltar.

Spanish Prime Minister Pedro Sanchez claimed the UK and European Union had agreed to its demands for guarantees over the status of Gibraltar in future negotiations.

Meanwhile Mrs May's political difficulties at home showed no sign of abating, with speculation that Remain-leaning Cabinet ministers have begun secret talks on a Brexit "Plan B" if the deal is rejected by MPs.

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The Sunday Times reported that Chancellor Philip Hammond - who warned on Saturday of "economic chaos" if there is no deal - is working with David Lidington, Amber Rudd, Greg Clark and David Gauke on trying to persuade Mrs May to adopt a softer Brexit which may be able to get through Parliament if her plan is rejected.

The Sunday Telegraph also reported that "several senior ministers" were working on plans for a Norway-style relationship with the EU.